Question

Question #0b4ea

Answer 1

To the nearest whole inch, the dimensions are 38 inches by 39 inches.

Explanation:

First, imagine a rectangle as the as the television. You can call the width `x` and the length `x+1`, since the problem states that the length is 1 more inch than its width.

The area of a rectangle is defined as its length times its height:

`A = l * w`
or you may have also seen
`A = b * h`

So for our television rectangle:

`A = (x+1)*x`

Using the distributive property, we can expand this:

`A = x^2 + x`

(Remember, `x` is the width of the TV.)

Now we can set this equal to what we want the area to be (1500 square inches):

`x^2 + x = 1500"in"^2`
or
`1x^2 + 1x -1500 = 0`

Using the quadratic formula, we can solve for `x`, our width:

`x = (-b +- sqrt(b^2-4ac))/(2a)`

`x = (-1 +- sqrt(1^2-4(1)(-1500)))/(2(1))`

`x = (-1 +- sqrt(1+6000))/2`

`x = (-1 +- sqrt(6001))/2`

`x ~~ 38.233061, -39.233061`

In this context, the negative answer (-39.233...) doesn't make sense because you can't have negative lengths on TV's, so you can ignore that answer and say that:

`x ~~ 38"in"`

Since `x` was our width and we know that our length is one inch longer than our width, the dimension must be 38 inches by 39 inches.